[verb て-form] + ちょうだい [verb ない-form] + で + ちょうだい
てちょうだい is a familiar "please do": the て-form of a verb plus ちょうだい, usually written in kana rather than as 頂戴. It sounds soft and a little motherly: you hear it mostly from women, and from adults speaking to children.
For "please don't", put ちょうだい after the ない-form plus で.
These go beyond ちょうだい after a verb.
On its own after a noun, ちょうだい means "give me". Children say it all the time.
The verb ちょうだい頂戴する is a formal humble word for "receive", the opposite end of the register from the request.